MR images are acquired in k-space in the Fourier domain. The acquired image data includes white noise. That is, noise in the acquired image data is a signal whose spectrum has equal power within any equal interval of frequencies. In order to transform the raw image data into an image, a reconstruction process is performed. Using a standard linear reconstruction model, one or more filtering operations must be performed during the reconstruction. During each filtering operation, multiplications may be performed to color the noise by making certain frequencies of the noise signal more prominent than others. This creates a modulation of the noise in the Fourier domain.
Following filtering, a coil combination process is performed to combine data acquired from individual coils of the MRI device. Coil combination may also encompass so-called “parallel imaging”, in which undersampling artifacts through accelerated acquisition are compensated for via dedicated coil combination coefficients. This combination may also amplify the noise in some region of the space, in the pixel domain. This noise “modulation” is often referred to as “G-factor” noise and may be influenced by the coil geometry, the field of view, the location of the imaging plane, and the sampling pattern used to acquire the k-space data. This creates modulation of the noise in space.
An additional modulation in the noise results from the signal level not being uniform in space. During imaging, a coil array is placed around the subject's body. Signal sensitivity is typically very good close to the coils (i.e., at the periphery of the body); however, sensitivity is poor in the center of image space. So, if an image is reconstructed based on this data, it will have a dark center region. To compensate for the difference in sensitivity, a corrective field may be applied in the pixel domain (i.e., multiply the pixel intensity by some factor in the center); however, this modulates the noise as well.
Accordingly, the noise associated with an MRI acquisition is Gaussian, but modulated in both in the Fourier domain and pixel domain. Conventional denoising techniques are unable to address denoising in this context because these techniques cannot adequately handle noise in the Fourier domain and, at the same time, adapt to varying noise level so denoising of the center of the image does not result in blurring.